Magnetic Interaction in Doped 2D Perovskite Cuprates with Nanoscale Inhomogeneity: Lattice Nonlocal Effects vs. Superexchange

We have studied the superexchange interaction $J_{ij}$ in doped $2D$ cuprates. The AFM interaction strongly depends on the state of the lattice of a CuO${}_2$ layer surrounded by two LaO rock salt layers. In a static U and D stripe nanostructure, the homogeneous AFM interaction is impossible due to the $U/D/U\dots$ periodic stripe sequence and $T_N=0$. In a dynamic stripe nanostructure, the ideal CuO${}_2$ layer with nonlocal effects and the homogeneous AFM interaction are restored. However, the interaction $J_{ij}$ decreases by the exponential factor due to partial dynamic quenching. The meaning of the transition from the dynamic to the static cases lies in the spontaneous $\theta$-symmetry breaking with respect to the rotation of all the tilted CuO${}_6$ octahedra by an orientation angle $\delta \theta =n·\left({45}^{°}\right)$ (where $n=1÷4$) in the U and D stripe nanostructure of the CuO${}_2$ layer. Moreover, the structural features help to study various experimental data on the charge inhomogeneity, Fermi level pinning in the p type cuprates only and time reversal symmetry breaking from a unified point of view.